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We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis demonstrates that, under these conditions, the perpetual put option consistently commands a higher price during periods of high volatility compared to those of low volatility. Moreover, we establish that the optimal exercise boundary is lower in high-volatility regimes than in low-volatility regimes. Additionally, we develop an analytical framework to describe American puts with an Erlang-distributed random-time horizon, which allows us to propose a numerical technique for approximating the value of American puts with finite expiry. We also show that a combined approach involving randomization and Richardson extrapolation can be a robust numerical algorithm for estimating American put prices with finite expiry.

This paper aims to study almost Ricci–Yamabe soliton in the context of certain contact metric manifolds.

The paper is designed as follows: In Section 3, a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator admitting almost Ricci–Yamabe soliton is considered. In Section 4, a complete K-contact manifold admits gradient Ricci–Yamabe soliton is studied. Then in Section 5, gradient almost Ricci–Yamabe soliton in non-Sasakian (k, μ)-contact metric manifold is assumed. Moreover, the obtained result is verified by constructing an example.

We prove that if the metric g admits an almost (α, β)-Ricci–Yamabe soliton with α ≠ 0 and potential vector field collinear with the Reeb vector field ξ on a complete contact metric manifold with the Reeb vector field ξ as an eigenvector of the Ricci operator, then the manifold is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field ξ. For the case of complete K-contact, we found that it is isometric to unit sphere S²ⁿ⁺¹ and in the case of (k, μ)-contact metric manifold, it is flat in three-dimension and locally isometric to Eⁿ⁺¹ × Sⁿ(4) in higher dimension.

All results are novel and generalizations of previously obtained results.

Throughout human history, the occurrence of disasters has been inevitable, leading to significant human, financial and emotional consequences. Therefore, it is crucial to establish a well-designed plan to efficiently manage such situations when disaster strikes. The purpose of this study is to develop a comprehensive program that encompasses multiple aspects of postdisaster relief.

A multiobjective model has been developed for postdisaster relief, with the aim of minimizing social dissatisfaction, economic costs and environmental damage. The model has been solved using exact methods for different scenarios. The objective is to achieve the most optimal outcomes in the context of postdisaster relief operations.

A real case study of an earthquake in Haiti has been conducted. The acquired results and subsequent management analysis have effectively assessed the logic of the model. As a result, the model’s performance has been validated and deemed reliable based on the findings and insights obtained.

Ultimately, the model provides the optimal quantities of each product to be shipped and determines the appropriate mode of transportation. Additionally, the application of the epsilon constraint method results in a set of Pareto optimal solutions. Through a comprehensive examination of the presented solutions, valuable insights and analyses can be obtained, contributing to a better understanding of the model’s effectiveness.

The interruption event will seriously affect the normal operation of urban rail transit lines,causing a large number of passengers to be stranded in the station and even making the train stranded in the interval between stations. This study aims to reduce the impact of interrupt events and improve service levels.

To address this issue, this paper considers the constraints of train operation safety, capacity and dynamic passenger flow demand. It proposes a method for adjusting small loops during interruption events and constructs a train operation adjustment model with the objective of minimizing the total passenger waiting time. This model enables the rapid development of train operation plans in interruption scenarios, coordinating train scheduling and line resources to minimize passenger travel time and mitigate the impact of interruptions. Regarding the proposed train operation adjustment model, an improved genetic algorithm (GA) is designed to solve it.

The model and algorithm are applied to a case study of interruption events on Beijing Subway Line 5. The results indicate that after solving the constructed model, the train departure intervals can be maintained between 1.5 min and 3 min. This ensures both the safety of train operations on the line and a good match with passengers’ travel demands, effectively reducing the total passenger waiting time and improving the service level of the urban rail transit system during interruptions. Compared to the GA algorithm, the algorithm proposed in this paper demonstrates faster convergence speed and better computational results.

This study explicitly outlines the adjustment method of using short-turn operation during operational interruptions, with train departure times and station stop times as decision variables. It takes into full consideration safety constraints on train operations, train capacity constraints and dynamic passenger demand. It has constructed a train schedule optimization model with the goal of minimizing the total waiting time for all passengers in the system.

Purpose – The research was carried out in order to study the composition of minerals, content of total-K, total-Ca, total-Mg, and exchangeable of K, Ca, Mg in volcanish ash from Sinabung volcano eruption.

Design/Methodology/Approach – The volcanic ash material in amount of 5 kg was collected from the depth of 0–20 cm and 21–41 cm. Mineral composition was determined by using line counting method; total contents of K, Ca, and Mg were measured by HCl 1N extraction, and exchangeable of K, Ca, and Mg was measured by NH₄OAc 1N pH 7.0 extraction.

Purpose – The results depicted in volcanic ash layer at the depth of 0–20 cm found some minerals such as plagioclase (34%), hypersthene (9%), augite (3%), hornblende/amphibole (5%), and volcanic glass (1%). These minerals were also found in different amounts at a depth of 21–41 cm. Hypersthene and amphibole were higher and augite was lower at a depth of 0–20 cm than 21–41 cm. The total content of K, Ca, and Mg was found to be 2.27%, 8.12%, and 2.28%, respectively, at a depth of 0–20 cm. The exchangeable of K, Ca, and Mg was found in an amount of 1.89 me/100 g, 20.71 me/100 g, and 1.62 me/100 g, respectively. The total content of K, Ca, and Mg was not available to plants but could potentially be as a source of plant nutrient after weathering while exchangeable form can be uptaken by plant directly.

Research Limitations/Implications – Based on the composition of the minerals, total, and exchangeable of K, Ca, and Mg that the material of volcanic ash, it could potentially be used as source of fertilizers.

Originality/Value – The composition of primary minerals contained in volcanic ash and to know the amount of elements K, Ca, and Mg-associated minerals either in total or exchange.

With the use of the grey incidence analysis (GIA), indicators such as the absolute degree of grey incidence (ε_ij), relative degree of grey incidence (r_ij) or synthetic degree of grey incidence (ρ_ij) are calculated. However, it seems that some assumptions made to calculate them are arguable, which may also have a material impact on the reliability of test results. In this paper, the authors analyse one of the indicators of the GIA, namely the relative degree of grey incidence. The aim of the article was to verify the hypothesis: in determining the relative degree of grey incidence, the method of standardisation of elements in a series significantly affects the test results.

To achieve the purpose of the article, the authors used the numerical simulation method and the logical analysis method (in order to draw conclusions from our tests).

It turned out that the applied method of standardising elements in series when calculating the relative degree of grey incidence significantly affects the test results. Moreover, the manner of standardisation used in the original method (which involves dividing all elements by the first element) is not the best. Much more reliable results are obtained by a standardisation that involves dividing all elements by their arithmetic mean.

Limitations of the conducted evaluation involve in particular the limited scope of inference. This is since the obtained results referred to only one of the indicators classified into the GIA.

In this article, the authors have evaluated the model of GIA in which the relative degree of grey incidence is determined. As a result of the research, the authors have proposed a recommendation regarding a change in the method of standardising variables, which will contribute to obtaining more reliable results in relational tests using the grey system theory.

In this paper, the authors prove that the Douglas space of second kind with a generalised form of special (α, β)-metric F, is conformally invariant.

For, the authors have used the notion of conformal transformation and Douglas space.

The authors found some results to show that the Douglas space of second kind with certain (α, β)-metrics such as Randers metric, first approximate Matsumoto metric along with some special (α, β)-metrics, is invariant under a conformal change.

The authors introduced Douglas space of second kind and established conditions under which it can be transformed to a Douglas space of second kind.

In this paper, the author introduces a degenerate exponential integral function and further studies some of its analytical properties. The new function is a generalization of the classical exponential integral function and the properties established are analogous to those satisfied by the classical function.

The methods adopted in establishing the results are theoretical in nature.

A degenerate exponential integral function which is a generalization of the classical exponential integral function has been introduced and its properties investigated. Upon taking some limits, the established results reduce to results involving the classical exponential integral function.

The results obtained in this paper are new and have the potential of inspiring further research on the subject.

The authors explore the hypothesis that some movements in commodity prices are anticipated (news shocks) and can trigger aggregate fluctuations in small open emerging economies. This paper aims to discuss the aforementioned objective.

The authors build a multi-sector dynamic stochastic general equilibrium model with endogenous commodity production. There are five exogenous processes: a country-specific interest rate shock that responds to commodity price fluctuations, a productivity (TFP) shock for each sector and a commodity price shock. Both TFP and commodity price shocks are composed of unanticipated and anticipated components.

The authors show that news shocks to commodity prices lead to higher output, investment and consumption, and a countercyclical movement in the trade-balance-to-output ratio. The authors also show that commodity price news shocks explain about 24% of output aggregate fluctuations in the small open economy.

Given the importance of both anticipated and unanticipated commodity price shocks, policymakers should pay attention to developments in commodity markets when designing policies to attenuate the business cycles. Future research should investigate the design of optimal fiscal and monetary policies in SOE subject to news shocks in commodity prices.

This paper contributes to the knowledge of the sources of fluctuations in emerging economies highlighting the importance of a new source: news shocks in commodity prices.

The purpose of this paper is to introduce a three-echelon multimodal transportation problem applied to a humanitarian logistic case study that occurred in Mexico.

This study develops a methodology combining a transshipment problem and an adaptation of the multidepot heterogeneous fleet vehicle routing problem to construct a mathematical model that incorporates the use of land-based vehicles and drones. The model was applied to the case study of the Earthquake on September 19, 2017, in Mexico, using the Gurobi optimization solver.

The results ratified the relevance of the study, showing an inverse relationship between transportation costs and delivery time; on the flip side, the model performed in a shorter CPU time with medium and small instances than with large instances.

While the size of the instances limits the use of the model for big-scale problems, this approach manages to provide a good representation of a transportation network during a natural disaster using drones in the last-mile deliveries.

The present study contributes to a model that combines a vehicle routing problem with transshipment, multiple depots and a heterogeneous fleet including land-based vehicles and drones. There are multiple models present in the literature for these types of problems that incorporate the use of these transportation modes; however, to the best of the authors’ knowledge, there are still no proposals similar to this study.